How do you find the dimensions of a rectangle whose perimeter is 46 cm and whose area is 128cm^2?
Do some quadratic equation solving to get a dimension of
We are looking for the length and width of this rectangle.
In order to find length and width, we need formulas which include length and width. Since we have perimeter and area, we will use the formulas for perimeter (
We can solve for either length or width - I'll start with width. Dividing by
We can substitute this into the equation for perimeter,
Since we know the perimeter is
Now divide everything by
Finally, rearrange and subtract
This is a quadratic equation whose solutions can be found using the quadratic formula:
We will use
As you can see, the rectangle seems to have two different possible lengths and widths, but they're actually the same. So the dimensions of the rectangle are